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A007800 From a problem in AI planning: a(n) = 4+a(n-1)+a(n-2)+a(n-3)+a(n-4)-a(n-5)-a(n-6)-a(n-7), n>7. 3
1, 2, 4, 8, 16, 31, 59, 111, 207, 384, 710, 1310, 2414, 4445, 8181, 15053, 27693, 50942, 93704, 172356, 317020, 583099, 1072495, 1972635, 3628251, 6673404, 12274314, 22575994, 41523738, 76374073, 140473833, 258371673, 475219609, 874065146 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The number of length n binary words with fewer than 3 zeros between any pair of consecutive ones. - Jeffrey Liese, Dec 23 2010
LINKS
T. Langley, J. Liese, and J. Remmel, Generating Functions for Wilf Equivalence Under Generalized Factor Order , J. Int. Seq. 14 (2011) # 11.4.2
FORMULA
a(1)=1, a(2)=2, a(3)=4, a(4)=8, a(5)=16, a(n)=3*a(n-1)-2*a(n-2)+0*a(n-3)- a(n-4)+ a(n-5). - Harvey P. Dale, Apr 24 2013
G.f.: -x*(x^4-x+1) / ((x-1)^2*(x^3+x^2+x-1)). - Colin Barker, Aug 18 2014
2*a(n) = A001590(n+4)-n. - R. J. Mathar, Aug 16 2017
MAPLE
for n from 1 to 5 do a[n]:= [1, 2, 4, 8, 16][n] od:
for n from 6 to 100 do a[n]:= 3*a[n-1]-2*a[n-2]-a[n-4]+a[n-5] od:
seq(a[n], n=1..100); # Robert Israel, Aug 19 2014
MATHEMATICA
LinearRecurrence[{3, -2, 0, -1, 1}, {1, 2, 4, 8, 16}, 40] (* Harvey P. Dale, Apr 24 2013 *)
PROG
(PARI) Vec(-x*(x^4-x+1)/((x-1)^2*(x^3+x^2+x-1)) + O(x^100)) \\ Colin Barker, Aug 18 2014
CROSSREFS
Cf. A062544.
Sequence in context: A106399 A334636 A299026 * A362063 A309982 A102726
KEYWORD
nonn,easy
AUTHOR
Peter Jonsson [ petej(AT)ida.liu.se ]
STATUS
approved

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Last modified May 18 16:47 EDT 2024. Contains 372664 sequences. (Running on oeis4.)